An Investigation of Haptic Perception of Viscoelastic Materials in the Frequency Domain

Although we hardly interact with objects that are purely elastic or viscous, haptic perception studies of deformable objects are mostly limited to stiffness and damping. Psychophysical investigation of materials that show both elastic and viscous behavior (viscoelastic materials) is challenging due to their complex, time and rate dependent mechanical behavior. In this study, we provide a new insight into the investigation of human perception of viscoelasticity in the frequency domain. In the frequency domain, the force response of a viscoelastic material can be represented by its magnitude and phase angle. Using this framework, we estimated the point of subjective equality (PSE) of a Maxwell arm (a damper and a spring in series) to a damper and a spring using complex stiffness magnitude and phase angle in two sets of experiments. A damper and a spring are chosen for the comparisons since they actually represent the limit cases for a viscoelastic material. We first performed 2I-2AFC adaptive staircase experiments to investigate how the perceived magnitude of complex stiffness changes in a Maxwell arm for small and large values of time constant. Then, we performed 3I-2AFC adaptive staircase experiments to investigate how the PSE changes as a function of the phase angle in a Maxwell arm. The results of our study show that the magnitude of complex stiffness was underestimated due to the smaller phase lag (with respect to a damper’s) between the sinusoidal displacement applied by the participants to the Maxwell arm and the force felt in their finger when the time constant was small, whereas no difference was observed for a large time constant. Moreover, we observed that the PSE values estimated for the lower bound of the phase angle were significantly closer to their actual limit (0◦) than those of the upper bound to 90◦.